Deformation-based interactive texture design using energy optimization

Transcription

1 Visua Comput (2007) 23: DOI /s ORIGINAL ARTICLE Jianbing Shen Xiaogang Jin Xiaoyang Mao Jieqing Feng Deformation-based interactive texture design using energy optimization Pubished onine: 13 June 2007 Springer-Verag 2007 J. Shen X. Jin ( ) J. Feng State Key Lab of CAD & CG, Zhejiang University, Hangzhou, , P.R. China {shenjianbing, jin, jqfeng}@cad.zju.edu.cn X. Mao University of Yamanashi, Japan mao@yamanashi.ac.jp Abstract In this paper, we present a nove interactive texture design scheme based on deformation and energy optimization. Given a sma sampe texture, the design process starts with appying a set of deformation operations to the sampe texture to obtain a set of deformed textures. Then oca changes to those deformed textures are further made by repacing their oca regions with the texture eements interactivey seected from other textures. Such a deform seect repace process is iterated many times unti the desired deformed textures are obtained. Finay the deformed textures are composed to form a arge texture with graph-cut optimization. By combining the graph-cut agorithm with an energy optimization process, interactive seections of oca texture eements are done simpy through indicating the positions of texture eements very roughy with a brush too. Our experimenta resuts demonstrate that the proposed technique can be used for designing a arge variety of versatie textures from a singe sma sampe texture, increasing or decreasing the density of texture eements, as we as for synthesizing textures from mutipe sources. Keywords Deformation Interactive Texture design Brushes Energy optimization 1 Introduction Textures have been a research focus for many years in human perception, computer graphics and computer vision. Recent decades of research activities in this area emphasize on texture synthesis. Given a sampe texture, a texture synthesis agorithm generates a new one bearing the same visua characteristics. In spite of the fact that numerous methods have been proposed for texture synthesis, how to design a variety of arge textures from a singe sma sampe texture is sti a chaenging probem. Recenty, Matusi et a. [18] deveoped a system for designing nove textures in the space of textures induced by an input database. However, their morphabe texture interpoation is based on a singe one-to-one warping between the pairs of texture sampes, which might be too restrictive for textures with highy irreguar structures, causing discontinuous mappings of the patches to the origina image. Shen et a. [22] proposed a competion-based texture design technique for producing a variety of textures by appying deformations to the extracted ayers of texture eements. The main imitation of Shen et a. s method, however, ies in the fact that it has no interaction with the oca property of the resuting texture eements. In this paper, we present a new deformation-based interactive texture design agorithm. The proposed agorithm has the abiity to ocay change the visua property of texture eements with itte user interaction, and hence drasticay broadens the variation of textures that can be synthesized with the existing methods. As shown in Fig. 1, from a singe sma sampe texture, our technique can create a variety of versatie textures, reguar or irreguar, with

2 632 J. Shen et a. increased or decreased density of texture eements. The main contributions of our work consist of the foowing three aspects: A nove framework for designing a arge variety of textures by integrating the techniques of 1) texture synthesis, 2) interactive image editing, 3) graph-cut based optimization, and 4) gradient-based Poisson optimization. An effective graph-cut and energy optimization-based method for automaticay extracting texture eements indicated by the designer. A new optimization based agorithm for synthesizing textures from mutipe sources. In the rest of the paper, we first introduce the reated work on texture synthesis and interactive image manipuation toos in Sect. 2. Then, in Sect. 3, we discuss the detais of our deformation and energy optimization-based interactive texture design scheme. The extension of the existing texture deformation agorithm using the competion technique is aso described in Sect. 3. The detais of the new graph-cut-based energy optimization method are given in Sect. 4, and the method for synthesizing textures from mutipe sources using optimization is presented in Sect. 5. After showing the experimenta resuts in Sect. 6, we concude the paper and show some directions for future work in Sect. 7. Fig. 1. Our deformation-based interactive texture design agorithm. a Sma input texture I; b1, b2, b3 the initia deformed textures I b1, I b2,...,i bk ; c1, c2, c3 the texture eements regions indicated by the designer s interactive brush; d1, d2, d3 the composed resut by oca deformations using energy optimization; e1, e2, e3 the interactive deformed textures I c1, I c2,...,i ck ; f1, f2 the designed textures I d1,i d2,...,i dk 2 Reated work Texture synthesis There is a ong sequence of earier papers on pixe-based and patch-based texture synthesis, which we can briefy review here. In non-parametric texture synthesis [6, 11], texture is synthesized one pixe (or one patch) at a time by finding pixes (patches) with simiar neighborhood to the aready synthesized pixes (patches) in the sampe texture. The traditiona approach is to generate textures sequentiay in a scanine order. Improvements incude hierarchica synthesis [25], coherent synthesis [9, 19], simiaritybased synthesis [4], feature matching and patch deformation synthesis [26], texton revisited synthesis [5], and appearance-space synthesis [15]. A number of authors have tacked the chaenge of combining and mixing textures. Efros and Freeman [11], Cohen et a. [6] and Kwatra et a. [14] synthesized a non-uniform texture composed of homogeneous patches. Wei et a. [24] generatedmixture oftexturesfrom mutipe input textures. Liu et a. [17] described a system to anayze and manipuate photographic textures that aows a user to design near reguar textures. Simiar to the work by Liu et a. [17], Matusik et a. [18] strived to buid a comprehensive texture mode, then constructed a texture space that spanned the range of textures induced by a database of natura images. The idea of appying transformations to the patches has aso been discussed by Kwatra et a. [14] in their patch-based texture synthesis technique using the graphcut agorithm. The resuts are obtained using deformation operations, such as rotation, mirror and scaing. However, as mentioned in their paper, the cost for searching matching patches wi increase when the extent of deformation increases. Shen et a. [22] proposed a competion-based texture design agorithm by appying transformations to

3 Deformation-based interactive texture design using energy optimization 633 the extracted texture ayers. Their technique can produce a wide variety of textures by making changes to the size, orientation and reative position of texture eements. However, the main imitation of their method ies in its inabiity to take into consideration the designer s need and creation. Interactions on oca texture eements are not aowed for the designers in their method. Interactive image manipuation toos Interactive image manipuation and editing packages, such as Adobe Photoshop, are commony utiized by digita photographers. In their workfow [21], images are manipuated directy and immediate visua feedback is provided. Recenty, many researchers proposed severa interactive digita image editing toos by using region-based methods, e.g., the magic wand in Photoshop [21], inteigent paint [2], interactive graph-cut image segmentation [3], azy snapping [16], and interactive image photomontage [1]. Our work is most cosey reated to the method of interactive digita montage [1], where users use brushes to indicate which parts of a set of photographs shoud be combined into a composite resut. Simiary, our method aso uses the strokes to define constraints for designing a variety of deformed textures. By aowing the user to interact with oca texture eements, our technique can provide oca changes to the size, orientation and reative position of texture eements according to the texture designer s need and creation. Moreover, our proposed agorithm has the abiity to increase or decrease the density of texture eements interactivey, which is suitabe for designing a variety of versatie textures from a singe sma sampe texture. 3 Our approach 3.1 Agorithm overview The goa of our agorithm is to enabe the texture designer to easiy create a deformed texture in a spatiay varying manner, aong with severa common types of deformation operations (rotation, transation, mirror, scae and fip). Our proposed workfow is summarized as foows: 1. Load a sma sampe texture image I. 2. Appy deformation operations (rotation, transation, mirror, scae and fip) to produce a set of sma deformed textures I b1, I b2,..., I bk. The range of rotation, transation and scae is interactivey controed by the designer. 3. Make oca changes to the deformed textures by copying oca texture eements from one to the other. 4. Design arge textures from the deformed textures obtained in Step (3) by using the graph-cut optimization agorithm. Appy further deformation operations if necessary. 5. Repeat Steps (2) to (4) unti a satisfactory set of textures I d1,i d2,...,i dk is obtained, combining the texture deformation agorithm described in Sect This workfow is iustrated by the sequence of images in Fig. 1. Given an input sampe texture (Fig. 1a), a set of deformed textures are produced (Fig. 1b1,b2,b3) after appying deformation operations. Then the user uses brushes to paint some texture eements interactivey (Fig. 1c1,c2,c3) and the corresponding regions of those texture eements are automaticay cacuated (Fig. 1d1,d2,d3). These texture eements are stitched into other textures with the gradient-based Poisson optimization [1, 20, 22], in order to obtain the textures with varying oca properties (Fig. 1e1,e2,e3). Finay, by appying the texture deformation agorithm described in Sect. 3.3 to the deformed textures, arge textures are designed (Fig. 1f1,f2). 3.2 Interactive oca texture deformation In order to make the above workfow effective, severa requirements shoud be met, such as quicky generated previews of the overa resut, a simpe, intuitive and easy to use mechanism for performing the oca deformation, and an undo function aowing the user to modify previousy specified adjustments. Our prototype impementation is based on the interactive digita photomontage technique [1] and supports severa types of brushes that can be used to set constraints for the texture s oca deformations. Simiary to [1], the designer uses the most frequenty used singe-texture brushes. At Step (3), the oca deformation of a texture is reaized by repacing its oca regions with the texture eements from another deformed texture. We ca the texture to be ocay deformed the base texture I base (I base {I, I b1, I b2,...,i bk }) and the texture providing the texture eements the reference texture I ref (I ref {{I, I b1, I b2,...,i bk } I base }). As shown in Fig. 1, the user does not need to precisey specify the region incuding the texture eements in I ref. Instead, the designer uses the brush to roughy paint the texture eements ( yeow fowers ) in I ref. The corresponding region incuding the texture eements is cacuated automaticay with the graph-cutbased energy optimization technique. The obtained texture eements are then embedded into to the base texture I base seamessy by the gradient-based Poisson optimization method [1, 22]. Such oca deformations are repeated severa times, whie at each step the user is aowed to choose new texture eements by painting new strokes according to his creation. The resuting base texture is further refined by the texture deformation agorithm using competion and then is used as the reference texture for another base texture. The descriptions of the texture deformation agorithm using competion and the graph-cut-based energy optimization technique can be found in Sects. 3.3 and 4, respectivey.

4 634 J. Shen et a. 3.3 Texture deformation using competion The ast step of our texture design workfow empoys the texture deformation agorithm using the competion technique [8, 22, 23], which is based on the method proposed in [22]. We refer the readers to [22] for a detaied description of their competion-based texture design method. The texture deformation agorithm using the competion technique is summarized as foows: Input: singe sampe texture I. Step 1: Layering, extracting texture ayers using existing coor image segmentation techniques [7, 12]. Step 2: Deformation, appying chaotic-based deformation operations (such as rotation, transation, mirror, fip and scae) to the texture ayers. Step 3: Exampe-based image competion, inpainting the hoe regions induced by deformation with the graph-cut agorithm. Step 4: Smoothing, removing the visua artifacts produced by Step 3 through the gradient-based Poisson optimization [1]. Output: deformed textures I 1, I 2,..., I k. In order to increase the versatiity of the deformed textures, we add a new fip operation to the set of deformation operations provided by [22]. Moreover, we extend it with more robust chaotic maps [13] beyond the basic ogistic map. The experimenta resuts demonstrate that our technique can generate a wide variety of arge deformed textures with a good stochastic property. 4 Interactive design using energy optimization Boykov et a. [3] have deveoped severa techniques that use the graph-cut agorithm for optimizing pixe abeing. Some eary vision probems, such as image restoration, can be modeed as an image abeing probem which is to find a abeing f that assigns each pixe p a abe f p,so that f is both piecewise smooth and consistent with the target data. Such a abeing f can be obtained as the resut of minimizing the foowing energy: Agarwaa et a. [1] used Boykov s graph-cut optimization agorithm for their interactive digita photomontage appication, where a new cost function is used to guide the optimization process resuting a smooth composition of source images. We further extend Agarwaa s work by empoying the energy optimization for texture montage. Suppose that we have obtained k deformed textures I b1, I b2,..., I bk after appying the deformation operations in the first step. We want to make oca changes to some of those textures by repacing their oca regions with the texture eements from remaining textures. As shown in Fig. 2, the user starts with seecting a base texture I base (Fig. 2a, the texture to be ocay changed) and the reference texture I ref (Fig. 2b, the texture providing the texture eements). After the user indicates the texture eements in I ref using brushes (Fig. 2c), a subimage I s (I s I ref ) encosing the brush stroke is cipped out from I ref. In order to produce the ocay deformed texture (Fig. 2f), we use the graph-cut based energy optimization agorithm to compute the abe of pixes in the composite texture (Fig. 2d) and find the best path (Fig. 2e) to smoothy stitch I s with I base. The abeing of the pixes in the composite texture is a mapping of the pixes between the base texture I base and the cipped reference texture I s.wedenote the abe for each pixe as L(p), it is certain that a seam (Fig. 2e) exists between two neighboring pixes (p, q) in the output if L(p) = L(q). In [1, 3], the energy function E for the abeing L of an image is defined as foows: E(L) = E data (L) + λ E smooth (L), (2) E data (L) = E d (p, L(p)), (3) p E smooth (L) = E s (p, q, L(p), L(q)), (4) p,q E( f ) = E smooth ( f ) + E data ( f ), (1) where E smooth measures the extent to which f is not piecewise smooth, whie E data measures the disagreement between f and the objective data. Boykov et a. [3] proposed an agorithm to find f through an iterative process. At each step, the graph-cut agorithm is used to find out the swapping between two abes α and β (α-β swap) or the assigning of a given abe (α-expansion) whie decreasing the energy E( f ) from that of the previous step. The abeing computation is guaranteed to be within a factor of two of the goba minimum when the cost function is a metric. Fig. 2a f. Iustration of our interactive design using energy optimization. a The base texture I base ; b the reference texture I ref ; c the position of the user s brush; d the cut region (with red boundary) incuding texture eements using our energy optimization method; e its corresponding abeing map; f the designed texture

5 Deformation-based interactive texture design using energy optimization 635 where the first term is defined by the distance to the image objective whie the second term is defined by the distance to the seam objective. Since we want to repace the oca region of the base texture with the specified texture eements in the reference texture, the image objective here is I s. Therefore E data (L) is computed as foows: { 0, if L(p) = Is E data (L) =, (5) v, if L(p) = I s where v is a user specified arge vaue. Since the abeing is a mapping to either I base or I s,the second term is defined by the distance between the pixes of I base and I s,thatis, E s (p, q, L(p), L(q)) = 0, if L(p) = L(q). (6) Otherwise, the energy is computed in the same way as [1]: E s (p,q, L(p), L(q)) M x, = M y, 0.5(M x + M y ) if coors if gradients, (7) if coors + gradients and G(p) is a six-component coor gradient (in R, G, B) at pixe p. The agorithm terminates when a pass over a abes fais to reduce the cost function. Kwatra et a. [14] and Agarwaa et a. [1] have successfuy used the apha expansion with this interaction penaty. In our case, we have aso found that it is good enough to produce satisfactory composite textures (Fig. 2f). 5 Texture design from mutipe sources using optimization Our texture design method from mutipe sources using optimization is extended from [24], but differs in that we perform patch-based synthesis via optimization whie theirs is based on pixe-by-pixe mixture. The goa of muti-source texture design is to synthesize new textures that capture the combined characteristics of severa input textures. For exampe, given four fower and grass textures (Fig. 6a), a set of new textures can be generated with a hybrid appearance (Fig. 6b ). where M x = C L(p) (p) C L(q) (p) + C L(p) (q) C L(q) (q), M y = G L(p) (p) G L(q) (p) + G L(p) (q) G L(q) (q), Fig. 3. Comparison of our deformation-based agorithm with image quiting [11], Wang ties [6] and graph-cut [14] Fig. 4. Comparison of our deformation-based agorithm with graphcut [14]

6 636 J. Shen et a. Fig. 5. Exampes of spatiay varying designed textures using our deformation-based method. Left coumns (a1, b1, c1, d1) are the input textures, the others are the deformed textures. Texture size: input: ; output: The detais of the proposed texture design agorithm from mutipe sources via optimization are described as foows: Input: mutipe texture sources {I 1, I 2,...,I k }. Step 1: Each source texture is divided into patches, and the source textures are represented by the patch sets: I 1 = { P I 1 1, P I 1 2,... },PI 1, I2 = { P I 2 1, P I 2 2,... },PI 2,...,I k = { P I k 1, P I k 2,... },PI k. Step 2: Randomy seect an initia patch P I k, paste it to the eft top corner of the output texture I mk, then find the best matched neighborhood patch P i constrained through optimizing the foowing function: min w i ( P I k ( P I k,p i ) ( P i + Ni P I k ) Ni (P i ) ), (8) where index i runs through a the input textures, N i (P I k ), N i (P i ) are the neighborhoods of P I k and P i, respectivey, and w i are the weights specified by the reative importance of the input sources. Step 3: Copy the best matched patch P i to the output texture I mk. Appy the graph-cut agorithm [3] to obtain a minimum-error-cut seam in the overapped region between P i and P I k. Step 4: Run Steps 2 to 3 iterativey unti the whoe output texture I mk is synthesized. The texture deformation

7 Deformation-based interactive texture design using energy optimization 637 Fig. 6. Designed textures from muti-source textures using our optimization agorithm. Texture size: input: ; output: using the competion technique described in Sect. 3.3 is then empoyed for further designing the deformed textures. Output: the fina designed textures {I m1, I m2,...,i mk }. 6 Experimenta resuts and discussions Our agorithm has been appied to a variety of sampe texture images. In our experiments, most of the source texture images are downoaded from the websites 1. For comparison, we use those sampe textures used by existing texture synthesis work [6, 11, 14]. A the experiments shown in this section were run on a PC with Pentium IV 1.6 GHz CPU MB RAM. In Fig. 3, we compare our approach with other existing techniques. The resut for graphcut was taken from [14], whie the other two were generated by our impementation. The texture size is for Fig. 3a, and for Fig. 3(b,c,d,e). The patch size is seected as From the images we find that the quaity of the texture generated with our approach is superior to that of image quiting [11] and Wang ties [6] and is comparabe to the resut produced by graphcut [14]. The sampe texture in Fig. 3a consists of ony two different otus fowers. The techniques that simpy use the origina patches seected from the sampe texture can ead to the repetition of those texture eements in the resuting arge texture. As shown in Fig. 3d, a the fowers have the same shape and orientation as either of the two fowers in the sampe texture. However, our interactive technique can create the texture consisting of the fowers of different shape, size and orientation, which is demonstrated in Fig. 3e. The density of the otus fowers in our resuts can be increased or decreased at the desired position according to the user s need. Figure 4 is another exampe demonstrating the effectiveness of our method, compared with the Graph-cut [14] method. As shown in Figs. 4c e, the density of texture eements (fowers) is increased (Fig. 4c and d) or decreased (Fig. 4e). Figure 5 gives more exampes demonstrating the capabiity of our technique for creating a arge variety of textures from a sma sampe, whie maintaining the continuity of texture features as we as the shapes of individua texture eements. Our method changes the density of texture eements (yeow fowers) interactivey according to the designer s need. In Fig. 5a2 a6, the density of the texture eements decrease graduay. We can aso interactivey make the eft part and the right part of the designed texture with different density (Fig. 5a3), create new texture eements (Fig. 5a5), ocay enarge the size of texture eements (Fig. 5a6), design reguar (Fig. 5a5,a6) or irreguar (Fig. 5a2 a4) texture patterns, and make the shape of designed texture ook ike a arge S shape (Fig. 5b5). Figure 6 demonstrates another interesting appication of our technique. Therein textures are synthesized from mutipe source textures using our optimization method. In Fig. 6, four input textures of size are used to interactivey create a variety of designed textures of size (Fig. 6b ). 7 Concusions and future work A nove deformation-based interactive texture design method using energy optimization has been proposed in this paper. Experimenta resuts demonstrate both the feasibiity and the effectiveness of our agorithm.

8 638 J. Shen et a. The main advantage of our agorithm over most existing texture synthesis methods ies in its capabiity to create a wide variety of very natura textures interactivey, from ony a singe sma sampe texture, according to the texture designer s need and creation. By appying the extended graph-cut-based energy optimization approach and the competion-based texture deformation method, we have designed textures with good stochastic property. Our experimenta resuts aso demonstrate that the proposed technique can be appied to other appications such as texture synthesis from mutipe sources. Athough the deformation operations used in our method can produce good resuts, it woud be meaningfu to deveop more sophisticated and powerfu deformation toos in the future. Another potentia extension of our method woud be its appication in dynamic texture design [10] where the consistency of the deformed textures between adjacent frames shoud be considered. Acknowedgement This work was supported by the China 973 program (Grant No. 2002CB312101), the China 863 program (Grant No. 2006AA-01Z314), the Nationa Natura Science Foundation of China (Grant No ), the Natura Science Foundation of Zhejiang Province (Grant No. R105431), the Program for New Century Exceent Taents in University (Grant No. NCET ), and the Ministry of Education, Science, Sports and Cuture, goverment of Japan, Grant-in-Aid for Scientific Research (B) (Grant No , 2006). The authors woud ike to thank Vivek Kwatra for making the Graphcut texture synthesis resuts avaiabe. References 1. Agarwaa, A., Dontcheva, M., Agrawaa, M., Drucker, S., Coburn, A., Curess, B., Saesin, D., Cohen, M.: Interactive digita photomontage. ACM Trans. Graph. 23(3), (2004) 2. Barrett, W.A., Cheney, A.S.: Object-based image editing. ACM Trans. Graph. 21(3), (2002) 3. Boykov, Y., Komogorov, V.: An experimenta comparison of min-cut/max-fow agorithms for energy minimization in vision. IEEE Trans. Patt. Ana. Mach. Inte. 26(9), (2004) 4. Brooks, S., Dodgson, N.: Sef-simiarity based texture editing. ACM Trans. Graph. 21(3), (2002) 5. Charaampidis, D.: Texture synthesis: textons revisited. IEEE Trans. Image Process. 15(3), (2006) 6. Cohen, M.F., Shade, J., Hier, S., Deussen, O.: Wang ties for image and texture generation. ACM Trans. Graph. 22(3), (2003) 7. Comaniciu, D., Meer, P.: Mean shift: A robust approach towards feature space anaysis. IEEE Trans. Patt. Ana. Mach. Inte. 24(5), (2002) 8. Criminisi, A., Pérez, P., Toyama, K.: Region fiing and object remova by exempar-based image inpainting. IEEE Trans. Image Process. 13(9), (2004) 9. Discher, J.-M., Maritaud, K., Lévy, B., Ghazanfarpour, D.: Texture partices. Comput. Graph. Forum. 21(3), (2002) 10. Doretto, G., Chiuso, A., Wu, Y., Soatto, S.: Dynamic textures. Int. J. Comput. Vision 51(2), (2003) 11. Efros, A.A., Freeman, W.T.: Image quiting for texture synthesis and transfer. In: Proceedings of SIGGRAPH 01, pp Los Angees, ACM, New York (2001) 12. Fezenszwab, P.F., Huttenocher, D.P.: Efficient graph-based image segmentation. Int. J. Comput. Vision 59(2), (2004) 13. Jakimoski, G., Kocarev, L.: Chaos and cryptography: bock encryption ciphers based on chaotic maps. IEEE Trans. Circ. Syst. 1: Fund. Theory App. 48(2), (2001) 14. Kwatra, V., Schöd, A., Essa, I., Turk, G., Bobick, A.: Graphcut textures: image and video synthesis using graph cuts. ACM Trans. Graph. 22(3), (2003) 15. Lefebvre, S., Hoppe, H.: Appearance-space texture synthesis. ACM Trans. Graph. 25(3), (2006) 16. Li, Y., Sun, J., Tang, C.K., Shum, H.Y.: Lazy snapping. ACM Trans. Graph. 23(3), (2004) 17. Liu, Y., Lin, W.C., Hays, J.H.: Near reguar texture anaysis and manipuation. ACM Trans. Graphics. 23(3), (2004) 18. Matusik, W., Zwicker, M., Durand, F.: Texture design using a simpicia compex of morphabe textures. ACM Trans. Graph. 24(3), (2005) 19. Nico, A., Meseth, J., Müer, G., Kein, R.: Fractiona Fourier texture masks: guiding near-reguar texture synthesis. Comput. Graph. Forum 24(3), (2005) 20. Pérez, P., Gangnet, M., Bake, A.: Poisson image editing. ACM Trans. Graph. 22(3), (2003) 21. Reichmann, M.: An image processing workfow. tutorias/workfow1.shtm 22. Shen, J.B., Jin, X.G., Mao, X.Y., Feng, J.Q.: Competion based texture design using deformation. Visua Comput. 22(9), (2006) 23. Shen, J.B., Jin, X.G., Zhou, C., Wang, C.C.L.: Gradient based image competion by soving the Poisson equation. Comput. Graph. 31(1), (2007) 24. Wei, L.Y.: Texture synthesis from mutipe sources. Proceedings of the SIGGRAPH 2003 Conference on Sketches & Appications. ACM, New York (2003) 25. Wei, L.Y., Levoy, M.: Fast texture synthesis using treestructured vector quantization. In: Proceedings of SIGGRAPH 00, pp New Oreans, ACM, New York (2000) 26. Wu, Q., Yu, Y.: Feature matching and deformation for texture synthesis. ACM Trans. Graph. 23(3), (2004)

9 Deformation-based interactive texture design using energy optimization 639 JIANBING SHEN is a PhD candidate of the State Key Lab of CAD&CG, Zhejiang University, Peope s Repubic of China. He received his BSc and MSc degrees in mechatronic engineering from Zhejiang University of Technoogy. His research interests incude texture synthesis, image competion, and high dynamic range imaging and processing. XIAOGANG JIN is a professor of the State Key Lab of CAD&CG, Zhejiang University. He received his BSc degree in computer science in 1989, MSc and PhD degrees in appied mathematics in 1992 and 1995, a from Zhejiang University. His current research interests incude impicit surface computing, specia effects simuation, mesh fusion, texture synthesis, crowd animation, coth animation and facia animation. XIAOYANG MAO is an associate professor at the University of Yamanashi in Japan. She received her MS and PhD degrees in computer science from Tokyo University. Her research interests incude fow visuaization, texture synthesis, non-photoreaistic rendering and human computer interactions. JIEQING FENG is a professor at the State Key Lab of CAD&CG, Zhejiang University, Peope s Repubic of China. He received his BSc degree in appied mathematics from the Nationa University of Defense Technoogy in 1992 and his PhD in computer graphics from Zhejiang University in His research interests incude space deformation, computer-aided geometric design and computer animation.